Would it be possible to add a way to check server status, number of active players, backup status and some other information for servers using modpacks or forge?

Server status is technically already a thing as the bot is only online when the server is online, number of online (not necessarily "active") players can be displayed on the playing status or topic of console/chat channel. Digging into forge information is probably never going to happen

Wouldn't it be possible to get this information directly from the website no?

..what website?

The Aternos site, it provides free servers, could they provide this information directly to DiscordSRV, overcoming this limitation of forge with the plugin?

That's much more unlikely to happen

Certainly won't be implemented